pcds (version 0.1.2)

IndNPEend1D: The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end interval case

Description

Returns \(I(x_2 \in N_{PE}(x_1,r))\) for points \(x_1\) and \(x_2\), that is, returns 1 if \(x_2\) is in \(N_{PE}(x_1,r)\), returns 0 otherwise, where \(N_{PE}(x,r)\) is the PE proximity region for point \(x\) with expansion parameter \(r \ge 1\) for the region outside the interval \((a,b)\).

rv is the index of the end vertex region \(x_1\) resides, with default=NULL, and rv=1 for left end interval and rv=2 for the right end interval. If \(x_1\) and \(x_2\) are distinct and either of them are inside interval int, it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops).

See also (ceyhan:metrika-2012;textualpcds).

Usage

IndNPEend1D(x1, x2, r, int, rv = NULL)

Arguments

x1

A 1D point whose PE proximity region is constructed.

x2

A 1D point. The function determines whether \(x_2\) is inside the PE proximity region of \(x_1\) or not.

r

A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).

int

A vector of two real numbers representing an interval.

rv

Index of the end interval containing the point, either 1,2 or NULL (default is NULL).

Value

\(I(x_2 \in N_{PE}(x_1,r))\) for points \(x_1\) and \(x_2\), that is, returns 1 if \(x_2\) is in \(N_{PE}(x_1,r)\) (i.e., if there is an arc from \(x_1\) to \(x_2\)), returns 0 otherwise

References

See Also

IndNPEmid1D, IndNCSmid1D, and IndNCSend1D

Examples

# NOT RUN {
a<-0; b<-10; int<-c(a,b)
r<-2

IndNPEend1D(15,17,r,int)
IndNPEend1D(15,15,r,int)

IndNPEend1D(1.5,17,r,int)

IndNPEend1D(-15,17,r,int)

IndNPEend1D(a,17,r,int)
IndNPEend1D(15,17,r=1.1,int)

a<-0; b<-10; int<-c(a,b)
r<-2
IndNPEend1D(15,17,r,int)

# }